Gaussian Unitary Ensembles with Pole Singularities Near the Soft Edge and a System of Coupled Painleve XXXIV Equations
Gaussian Unitary Ensembles with Pole Singularities Near the Soft Edge and a System of Coupled Painleve XXXIV Equations
复制标题
软边附近具有极奇点的高斯酉系综和耦合 Painleve XXXIV 方程组
DOI：
10.1007/s00023-019-00834-y
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发表时间：
2019
影响因子：
1.5
通讯作者：
Zhang Lun
中科院分区：
文献类型：
--
作者：
Dai Dan;Xu Shuai Xia;Zhang Lun
In this paper, we study the singularly perturbed Gaussian unitary ensembles defined by the measure $$\begin{aligned} \frac{1}{C_n} \mathrm{e}^{- n\text {tr}\, V(M;\lambda ,\mathbf {t}\;)}\mathrm{d}M, \end{aligned}$$over the space ofHermitian matricesM, wherewith, in the multiple scaling limit, wheretogether withasat appropriate related rates. We obtain the asymptotics of the partition function, which is described explicitly in terms of an integral involving a smooth solution to a new coupled Painlevé system generalizing the Painlevé XXXIV equation. The largenlimit of the correlation kernel is also derived, which leads to a new universal class built out of the-function associated with the coupled Painlevé system.
In this paper, we study the singularly perturbed Gaussian unitary ensembles defined by the measure $$\begin{aligned} \frac{1}{C_n} \mathrm{e}^{- n\text {tr}\, V(M;\lambda ,\mathbf {t}\;)}\mathrm{d}M, \end{aligned}$$over the space ofHermitian matricesM, wherewith, in the multiple scaling limit, wheretogether withasat appropriate related rates. We obtain the asymptotics of the partition function, which is described explicitly in terms of an integral involving a smooth solution to a new coupled Painlevé system generalizing the Painlevé XXXIV equation. The largenlimit of the correlation kernel is also derived, which leads to a new universal class built out of the-function associated with the coupled Painlevé system.